Multiply the following complex numbers: $({4+4i}) \cdot ({-3i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({4+4i}) \cdot ({-3i}) = $ $ ({4} \cdot {0}) + ({4} \cdot {-3}i) + ({4}i \cdot {0}) + ({4}i \cdot {-3}i) $ Then simplify the terms: $ (0) + (-12i) + (0i) + (-12 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (-12 + 0)i - 12i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (-12 + 0)i - (-12) $ The result is simplified: $ (0 + 12) + (-12i) = 12-12i $